The effect of three-dimensional confinement on the size and morphology of a vesicular surfactant mesophase obtained by mixing micellar solutions of cetyltrimethylammonium bromide and dodecylbenzenesulfonic acid has been studied using small-angle neutron scattering (SANS). The confined spaces were generated by the random close packing of polystyrene beads of radius R-b = 1.5, 0.25, and 0.1 mu m, creating voids of characteristic dimensions R similar to 0.22 R-b = 3300, 550, and 220 angstrom, respectively. These void length scales were comparable to or less than the radii of vesicles formed in the system under conditions of no confinement. Vesicles, made by mixing 0.8 wt % micellar solutions of surfactant in a water/D2O mixture that is contrast-matched with the polystyrene beads, were added in a SANS scattering cell without beads, as well as three cells with the different sized beads. The SANS data from the sample without confinement was best fitted by a core-shell model and not by spheres or disks, confirming the presence of vesicles. The data from samples in the confined domains also showed vesicles as the dominant structure. The most important result is that the mean size of these vesicles decreases as the confinement length scale is reduced. A simple thermodynamic model accounting for the balance between increased enthalpy when vesicles with curvature higher than the preferred one are formed, and increased free volume entropy for smaller vesicles supports the experimental data. While these results are focused on a specific vesicle system, the broad principles behind changes in microstructure produced by confinement are applicable to other surfactant aggregates. The results of this study are potentially important for understanding the flow of drug delivery vehicles through microcapillaries, in the recovery of oil from fine pores in rocks using surfactant containing fluids, micellar enhanced ultrafiltration, or in other situations where the size of surfactant aggregate structures approach the length scales between confining walls.